Julia set · complex dynamics

BOUNDED, OR GONE FOREVER

zn+1 = zn2 + c c = −0.000 + 0.000 i

Take a point in the complex plane, square it, add c, and do it again forever. Either the sequence stays bounded or it runs away to infinity — and the boundary between those two fates is this shape. It is infinitely detailed at every magnification. Here c walks a slow closed loop, and the whole figure dissolves and re-forms as it goes.